I would guess that someone saw a colt sucking on *something* hanging from it's mothers underside. Humans, curious as we are, probably went in to figure out what was happening. It's not a far leap then to think that someone figured "hey, if that cow can drink it, I bet I can drink it", and so they tried it and from there it caught on.

Maybe they saw calf's drinking from their mom's? Honestly, cow's milk is probably one of the least astonishing foods to have been eaten. Back in the day, there was probably some sort of amount of eating raw flesh. Now who among you would look at a cow and think, wow that looks tasty... let me go kill that, pull out it's hair and sink my teeth in? Also, think about things like octopus... goose liver... caviar... peanuts... it's pretty interesting.

"I would guess that someone saw a colt sucking on *something* hanging
from it's mothers underside. Humans, curious as we are, probably went
in to figure out what was happening."

I don't think they had to figure out what was happening. Humans are mammals. Cows are mammals. Humans drink their mothers' breastmilk when they are young. Calfs drink their mothers' breastmilk when they are young.

Mr. Ask Jeeves, I'm pretty sure humans realized that all furry animals feed their offspring with breastmilk from the females' nipples long before they had to chop of an animal and see which liquids spilled out.

are you basing anything off of history Rensmouth? The Truth will never be out there because something like that was never recorded in any text's. And Humans for that time period were Tribes of family's so yes my theory if it can be called a theory is not off base.

Which came first: the domestication of cows, or mothers breastfeeding their children?

The breastfeeding. Way, way before. Millions of years before. Humans did it long before they ever came in contact with the ancestors of our modern cows. They did it when hunting mammoths. They did it when we as a species were scavengers on the African plains picking meat off of bones left behind by larger predators.

Do you honestly think that humans would be surprised to see cows breastfeeding when they observed the exact same occurrence happening between every species of mammals they came across? Do you honestly think humans were not smart enough to make the following analysis:

My wife and the mother of my child feeds our baby by letting him drink milk from her breasts where a little nipple sticks out. This cow feeds her calf by letting it drink milk from her breasts nipples stick out. My baby is sustained by my wife's breastmilk. This calf is sustained by its mother's breastmilk. Therefore, it is very well possible I could be sustained by the cow's breastmilk.

Do you honestly believe humans had to cut a mother cow up to discover that it had a liquid inside it not too different from human breastmilk? It's a quite unnecessary step, and as cows would probably one of the more recent species humans have come across in our evolutionary history, early humans already had thousands of years to witness breastfeeding among mammals.